Spherical K-Means and Elbow Method Optimizations With Fisher Statistics for 3D Stochastic DFN From Virtual Outcrop Models

Abstract

Fracture modeling plays a valuable role to understand the fluid flow in carbonate reservoirs. For this, the fracture characterization to generate Discrete Fracture Networks (DFNs) can take advantage of analogue outcrops through Virtual Outcrop Models (VOMs), acquired by Unmanned Aerial Vehicles (UAV) and digital photogrammetry. The stochastic DFN generation is an important step in reservoir modeling as it brings more representative data to the process and has long been studied. However, optimizations concerning automatizing some of the steps necessary to its generation like data clustering are still open to advancements. In this sense, this work aims the fracture data clustering and the definition of the number of clusters when gathering data for the stochastic process, developing an Elbow method for spherical data and a balanced K-means, both based on Fisher statistics. For this, we interpreted fracture planes in a VOM that recreates a carbonate reservoir analogue from the Jandaíra Formation, in the Northeast, Brazil. As result, we show a workflow for immersive fracture interpretation alongside a 3D stochastic DFN model with fracture intensity of 22.57m^-1 for cell sizes of 1m³. Regarding the clustering balance, our method achieved a lower standard deviation between sets while maintaining the Fisher values greater to obtain fracture sets with lower dispersion. Additionally, the Elbow method implementation proved a beneficial step to the workflow as it reduced the interpretation bias of family clusters. These results alongside the proposed workflow bring a better understanding of the outcrop geometry while offering data scalability for reservoir modeling.